Bring a large pot of salted water to a boil for the pasta.
Peel and cut all the vegetables into equal pieces. Cut the carrots and parsnips into thin strips, the leeks into long strips, the courgette into half slices, the bell pepper into strips, the broccoli or bimi into bite-sized pieces, the garlic into thin slices, and the chili pepper finely.
Heat 2 tablespoons of olive oil in a large pan. Sauté the garlic and chili pepper over low heat until fragrant and lightly browned. Remove from the pan and set aside.
If necessary, add another small splash of oil to the same pan and fry the carrot, parsnip, leek, courgette, bell pepper, and broccoli or bimi over high heat. Stir-fry them briefly so that they remain al dente but still get some color. Season with pepper and a little salt. Set aside with the garlic and chili.
Meanwhile, cook the whole wheat spaghetti al dente according to the package instructions. Set aside at least 1 cup of pasta water and then drain the pasta.
In a bowl, whisk together the egg yolks, Parmesan cheese, 2 tablespoons olive oil, lemon zest, some black pepper, and 2 to 3 tablespoons warm pasta water until creamy.
Return the warm pasta to the cooking pot or pan, but remove it from the heat first. Add the egg mixture and stir well immediately. Gradually add the extra pasta water until you get a glossy, creamy sauce. If necessary, set it to very low heat for a very short time, but definitely do not let it boil.
Mix the sautéed vegetables, garlic, and chili into the pasta. Add lemon juice to taste and finish with extra Parmesan cheese, a drizzle of olive oil, and optionally some fresh parsley or basil.
Serve immediately.